Variation of Hodge structures for non-K\"ahler manifolds

Wei Xia

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arXiv · 2205.09274

Variation of Hodge structures for non-K\"ahler manifolds

Wei Xia

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Abstract

In this note, we discuss unpolarized, complex variation of Hodge structures for non-K\"ahler manifolds. In particular, given a holomorphic family of compact complex manifolds whose central fiber satisfies: the inclusions $F^{p}A^{p+q+1}(X)\hookrightarrow A^{p+q+1}(X), F^{p}A^{p+q}(X)\hookrightarrow A^{p+q}(X)$ are injective in cohomology, it is shown that the period map is holomorphic and transversal.

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Wei Xia. 2022-05-19. Variation of Hodge structures for non-K\"ahler manifolds. https://arxiv.org/abs/2205.09274

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